Geometric stability of the many-body localized phase in two and higher dimensions

Isolated disordered quantum systems need not equilibrate and be described by statistical mechanics; this is the phenomenon of many-body localization (MBL). In higher dimensions, the existence of MBL is a delicate question due to the possibility of inclusions of lower dimensional "thermal" regions. In this talk, I will argue that MBL is stable in higher dimensions by analyzing the geometry of a MBL insulator coupled to a thermal edge and develop a phenomenology of such systems.